Related papers: Shinohara Rock-Paper-Scissors
Classic Rock-Paper-Scissors, RPS, has seen many variants and generalizations in the past several years. In the previous paper, we defined playability and balance for games. We used these definitions to show that different forms of imbalance…
Rock-Paper-Scissors (RPS), a game of cyclic dominance, is not merely a popular children's game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no…
Consider the following variant of Rock, Paper, Scissors (RPS) played by two players Rei and Norman. The game consists of $3n$ rounds of RPS, with the twist being that Rei (the restricted player) must use each of Rock, Paper, and Scissors…
In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an…
In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth nothing and a tie worth 1, and the payoff of winning (the incentive a) as a variable, this game is called as generalized RPS game. The generalized RPS game is a…
We generalize Rock Paper Scissors to complete directed graphs, or tournaments, on $n$ vertices. Properties of the mixed-strategy Nash equilibria of these tournaments are discussed, particularly those with Nash equilibria where all of the…
The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely studied in terms of its theoretical analysis as well as in its applications, ranging from sociology and biology to economics. Many experimental results of the RPS…
We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game from the point of view of evolutionary stability. In its classical version the game has a mixed Nash equilibrium (NE) not stable against mutants. We find a…
The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…
Spiro, Surya and Zeng (Electron. J. Combin. 2023; arXiv:2207.11272) recently studied a semi-restricted variant of the well-known game Rock, Paper, Scissors; in this variant the game is played for $3n$ rounds, but one of the two players is…
Predicting and modeling human behavior and finding trends within human decision-making processes is a major problem of social science. Rock Paper Scissors (RPS) is the fundamental strategic question in many game theory problems and…
Social dilemmas concern a natural conflict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the…
How humans make decisions in non-cooperative strategic interactions is a challenging question. For the fundamental model system of Rock-Paper-Scissors (RPS) game, classic game theory of infinite rationality predicts the Nash equilibrium…
We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…
We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously…
The Rock-Paper-Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained…
The Reward-Penalty-Selection Problem (RPSP) can be seen as a combination of the Set Cover Problem (SCP) and the Hitting Set Problem (HSP). Given a set of elements, a set of reward sets, and a set of penalty sets, one tries to find a subset…
It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors…
We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study…
The Rock-Scissors-Paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic…